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# the1 - Middle East Technical University Department of...

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Middle East Technical University Department of Computer Engineering CENG 140 Fall 2010-2011 Take Home Exam 1 REGULATIONS Due date: 29 November, 2010 Monday (Not subject to postpone) Submission: Electronically. You will be submitting your program source code through a text file which you will name as the.c by means of the COW system. Team: There is no teaming up. The homework has to be done and turned in individually. Cheating: The source(s) and the receiver(s) will receive zero and be subject to disciplinary action. BACKTRACKING Backtracking is a widely-used method in Computer Science for finding a solution to a problem incrementally. The current (partial) solution is usually kept as an ordered set V = v 1 , .., v N and at each step, a new partial- solution-element v i is added to V in such a way that the addition of v i to V approaches us one step closer to the complete solution and that v i is not in conflict with V as far as the problem is concerned. If V + v i is invalid, another element, if there is any, is placed in the position of v i . If no v can be found that would make V + v valid, the algorithm backtracks ; in other words, it goes back to the previous step and tries another element v ; in our scenario, this would mean removing v LAST and placing some other v in v LAST ’s place that would not invalidate V . The process of (i) adding a valid new partial solution, and (ii) backtracking to find a valid new partial solution is repeated until a solution is found or all the possible options are exhausted, which means that no valid solution exists for the problem.

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